Geodesic
The method of the characteristic parallelogram of the solution of the second mixed problem for the one-dimensional wave equation
Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 43-53

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The authors of the article wrote the solution of the second mixed problem for the one-dimensional wave equation in the form of a formula convenient for numerical realization using the characteristic parallelogram. The derivation of this formula is based on the representation of the classical solution of the problem. 
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     title = {The method of the characteristic parallelogram of the solution of the second mixed problem for the one-dimensional wave equation},
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V. I. Korzyuk; S. N. Naumavets; V. P. Serikov. The method of the characteristic parallelogram of the solution of the second mixed problem for the one-dimensional wave equation. Trudy Instituta matematiki, Tome 26 (2018) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/TIMB_2018_26_1_a7/